부산대학교 도서관

When aiming to apply mathematical results of non-commutative geometry to physical problems the question arises how they translate to a context in which only a part of the spectrum is known. In this article we aim to detect when a finite-dimensional triple is the truncation of the Dirac spectral triple of a spin manifold. To that end, we numerically investigate the restriction that the higher Heisenberg equation [A. H. Chamseddine, A. Connes, and V. Mukhanov, Journal of High Energy Physics, 98 (2014)] places on a truncated Dirac operator. We find a bounded perturbation of the Dirac operator on the Riemann sphere that induces the same Chern class.
Comment: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Journal of Mathematical Physics 61, 033507 (2020) and may be found at https://doi.org/10.1063/1.5131864